A, B and C were partners sharing profits in the ratio of 1/5, 1/3 and 7/15 respectively. C retires and his share is taken up by A and B in the ratio of 3:2. Find out the new profit sharing ratio and gaining ratio of A and B.
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Old ratio (P, Q, and R) = 1/5, 1/3 and 7/15 or 3 : 5 : 7
R's profit share = 7/15
P and Q decided to take his share in the ratio of 3 : 2
Share of R taken by P = (7/5) *(3/5) = 21/75
Share of R taken by Q = (7/5) * (2/5) = 14/75
New profit share = Old profit share + Share taken from R
P's new share = (3/15) + (21/75) = (15 + 21)/75 = 36/75
Q's new share = (5/15) + (14/75) = (25 + 14)/75 = 39/75
New profit sharing ratio (P and Q) = 36:39 = 12:13
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